Question

If the parabola of the form y = a(x – h)2 + k is always shifted horizontally h units and vertically k units, then its vertex is always
(–h, –k)

(h, k)

(–h, k)

(h, –k)

Answer 1

The vertex of the transformed parabola with the equation $y=a(x-h)^2+k$ is (h, k).

What are the transformation rules for horizontal and vertical shifts?

The transformation rules are:

Translation: (x, y) → (x + a, y) or (x, y) → (x - a, y) (Horizontal shift)

Translation: (x, y) → (x , y + b) or (x, y) → (x , y - b) (Vertical shift)

Calculation:

It is given that, the transformed parabola is $y=a(x-h)^2+k$

This parabola has vertex at (h, k).

Since this equation is obtained by shifting h units horizontally and k units vertically.

So, the original vertex is at (h - h, k - k) = (0, 0)

Thus, the equation of the actual parabola is $y=ax^2$

Therefore, the given transformed equation of parabola has vertex (h, k).

Learn more about transformation rules here:

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